{
  "id": "2406.09587",
  "version": "v1",
  "published": "2024-06-13T20:57:39.000Z",
  "updated": "2024-06-13T20:57:39.000Z",
  "title": "On the long time behaviour of solutions to the Navier-Stokes-Fourier system on unbounded domains",
  "authors": [
    "Elisabetta Chiodaroli",
    "Eduard Feireisl"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Navier-Stokes-Fourier system on an unbounded domain in the Euclidean space $R^3$, supplemented by the far field conditions for the phase variables, specifically: $\\rho \\to 0,\\ \\vartheta \\to \\vartheta_\\infty, \\ u \\to 0$ as $\\ |x| \\to \\infty$. We study the long time behaviour of solutions and we prove that any global-in-time weak solution to the NSF system approaches the equilibrium $\\rho_s = 0,\\ \\vartheta_s = \\vartheta_\\infty,\\ u_s = 0$ in the sense of ergodic averages for time tending to infinity. As a consequence of the convergence result combined with the total mass conservation, we can show that the total momentum of global-in-time weak solutions is never globally conserved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-13T20:57:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long time behaviour",
      "navier-stokes-fourier system",
      "unbounded domain",
      "global-in-time weak solution",
      "far field conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}